Strongly coupled linear hyperbolic systems modelling of multi-layered solid body applications in Geophysics
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 41, No 4, (2015), 513p-526p
In this paper is given a new approach to 3D modelling of elastic piecewise homogeneous media, in particular Earth crust and upper Mantle. The method is based on the principle of tomography with Earthquake as a source of the signal and at least three receiver stations on the surface. The wave propagation in such media is described by a system of three strongly coupled hyperbolic equations with piece-wise constant coefficients. The characteristic set and bi-characteristic curves are computed in a homogeneous half-space with free boundary as well as the formulae of reflection and diffraction of the bi-characteristics on the internal boundaries of the media. Applications of the characteristic set and bi-characteristic curves for the inverse problem in geophysics and Earth modelling are given. 2010 Mathematics Subject Classification: 35L53, 35Q86, 86A15.